Technical Note: TIGRE-DE for the Creation of Virtual Monoenergetic images from Dual-Energy Cone-Beam CT

Abstract

Background

Dual-energy (DE)-CBCT represents a promising imaging modality that can produce virtual monoenergetic (VM) CBCT images. VM images, which provide enhanced contrast and reduced imaging artifacts, can be used to assist in soft-tissue visualization during image-guided radiotherapy.

Purpose

This work reports the development of TIGRE-DE, a module in the open-source TIGRE toolkit for the performance of DE-CBCT and the production of VM CBCT images. This module is created to make DE-CBCT tools accessible in a wider range of clinical and research settings.

Methods

We developed an add-on (TIGRE-DE) to the TIGRE toolkit that performs DE material decomposition. To verify its performance, sequential CBCT scans at 80 kV and 140 kV of a Catphan 604 phantom were decomposed into equivalent thicknesses of aluminum (Al) and polymethyl-methylacrylate (PMMA) basis materials. These basis material projections were used to synthesize VM projections for a range of x-ray energies, which were then reconstructed using the Feldkamp-Davis-Kress (FDK) algorithm. Image quality was assessed by computing Hounsfield units (HU) and contrast-to-noise ratios (CNR) for the material inserts of the phantom and comparing with the constituent 80 kV and 140 kV images.

Results

All VM images generated using TIGRE-DE showed good general agreement with the theoretical HU values of the material inserts of the phantom. Apart from the highest-density inserts imaged at the extremes of the energy range, the measured HU values agree with theoretical HUs within the clinical tolerance of ±50 HU. CNR measurements for the various inserts showed that, of the energies selected, 60 keV provided the highest CNR values. Moreover, 60 keV VM images showed average CNR enhancements of 63% and 66% compared to the 80 kV and 140 kV full-fan protocols.

Conclusions

TIGRE-DE successfully implements DE-CBCT material decomposition and VM image creation in an accessible, open-source platform.

1. Introduction:

Cone-beam CT (CBCT) is used to assist in patient positioning during image-guided radiotherapy (IGRT) and shows potential to serve as an imaging modality in more advanced applications such as on-line re-planning for adaptive radiotherapy (ART) through soft-tissue visualization.^1–5 While CBCT can be obtained from the on-board imager (OBI) mounted directly to the linac gantry, it generally has low soft tissue contrast and other image artifacts may be visible.^6–8 Dual-energy (DE) techniques have the potential to alleviate some of these difficulties encountered in conventional CBCT imaging, notably in the ability to create virtual monoenergetic (VM) images which show enhanced image contrast and reduced artifacts such as beam hardening. DE-CBCT also allows for the direct computation of electron density images with higher accuracy than conventional methods.⁹ However, while several groups have explored the viability of DE-CBCT, they have largely focused on proof-of-principle studies.^10–13 Reports exploring applications of DE-CBCT methods in the clinical setting remain sparse.¹⁴ One potential cause of this sparsity of DE-CBCT clinical data is that DE-CBCT material decomposition is performed using either in-house or proprietary software, such as Varian’s iTools Reconstruction.¹² Limited access to the tools used to perform DE-CBCT analysis has hindered the advancement of these techniques.

Recently, open-source CBCT reconstruction initiatives have become available that show the potential to obviate these accessibility problems. Several toolkits are available, including AirTools II¹⁵, ASTRA¹⁶, CASTOR¹⁷, RTK¹⁸, and TIGRE.¹⁹ While these toolkits focus primarily on the image reconstruction process, the implementation of additional CBCT functionality represents a natural extension. Recent work on the TIGRE toolkit, for example, has added modules specifically designed to carry out pre-processing and post-processing methods.²⁰ Our work develops and introduces the TIGRE-DE module, an accessible, open-source module for performing the construction of VM CBCT images from DE-CBCT. This module is implemented within the wider TIGRE toolkit, furthering the ability of researchers and clinicians to access cutting-edge work in CBCT image production and processing. The creation of accessible tools for DE-CBCT will help facilitate further development of DE-CBCT as a clinically relevant imaging technique.

2. Materials and Methods:

DE-CBCT involves the acquisition of image projections at two distinct energies. The projections can then be decomposed into linear combinations of various basis materials to model the energy dependence of the attenuation values. These basis materials can be subsequently used to synthesize virtual monoenergetic (VM) images. VM images represent the response of the imaged object to monoenergetic x-rays in contrast, to the polychromatic x-rays produced by conventional x-ray tubes. Compared with polychromatic kV images, VM images are expected to show enhanced soft-tissue contrast as well as reduced beam hardening and metal artifacts.¹³ The theory has been described in depth by several authors^{12,13,21–24}, so only a brief overview of the general principle is presented below.

2.1. Basis material decomposition

At the energies used in CBCT imaging, the attenuation of x-rays is due to the photoelectric effect and Compton scattering. To produce VM images, a common technique involves decomposing the specific material contributions to the x-ray attenuation into a linear combination of two basis materials, one high-Z to model the contribution of the photoelectric effect, and one low-Z to model the contribution of Compton scattering. Though many different combinations can be selected as basis materials, decompositions performed in the projection domain commonly choose aluminum (Al) and polymeythyl-methylacrylate (PMMA), respectively, to model these effects, as shown in Eq. (1):^12,13,21,24

$$-\ln \frac{I}{I_0}=\sum {\mu }_i{x}_i={\mu }_{Al}{x}_{Al}+{\mu }_{PMMA}{x}_{PMMA}.$$ (1)

Here $I_0$ and $I$ are the incident and resultant x-ray intensities forming each projection, ${\mu }_i$ and $x_i$ represent the attenuation coefficients and thicknesses, respectively, for each voxel in the image volume along the x-ray path, ${\mu }_{\mathrm{A}\mathrm{l}}$ and ${\mu }_{PMMA}$ represent the attenuation coefficients of the chosen basis materials Al and PMMA, and $x_{Al}$ and $x_{PMMA}$ are the equivalent thicknesses of Al and PMMA along the x-ray path.

In principle, since $\mu$ is a function of energy, determining the equivalent thicknesses of the basis materials $x_{Al}$ and $x_{PMMA}$ for a given object is just a matter of obtaining attenuation measurements at two different imaging energies and solving the resulting system of Eqs. (1) for the equivalent thickness values. In practice, however, x-ray tubes produce a spectrum of polychromatic x-rays rather than the monochromatic x-rays assumed above. Solving the resulting system of equations thus requires integrating over the energy spectra and makes analytical solutions for $x_{Al}$ and $x_{PMMA}$ difficult to obtain even in cases where the spectra are known exactly.

An alternative approach^12,13,22 seeks numerical solutions for $x_{Al}$ and $x_{PMMA}$. The equivalent thicknesses $x_{Al}$ and $x_{PMMA}$ can be expressed as a set of third-degree polynomials [as in Eq. (2)]:

$$x_i=a_{1,i}L+a_{2,i}H+a_{3,i}{L}^2+a_{4,i}LH+a_{5,i}{H}^2+a_{6,i}{L}^3+a_{7,i}{L}^{2}H+a_{8,i}L{H}^2+a_{9,i}{H}^3.$$ (2)

Here the $i$ subscript refers to Al or PMMA, as appropriate. $L$ and $H$ refer to the measured x-ray attenuation values for the low- and high-energy x-ray tube voltages, respectively, and is given by:

$$L=-\ln \left(\frac{I_l}{I_{0,l}}\right),H=-\ln \left(\frac{I_h}{I_{0,h}}\right).$$ (3)

2.1.1. Calibration of Basis Material Thicknesses

The coefficients $a_{n,i}$ need to be calibrated by measuring the attenuation values of known thickness combinations of Al and PMMA. In this work, a virtual step-wedge phantom was used to compute the attenuation values of various combinations of Al and PMMA thicknesses.¹² For each material thickness pair of this virtual phantom, the theoretically expected scatter-free attenuation measurement is calculated by integrating over the kV source spectrum combined with the Monte-Carlo-derived detector efficiency and the material attenuation spectra of the basis materials. The Al thickness in this step-wedge phantom was varied from 0 to 160 mm in 1 mm increments, while the PMMA thickness was independently varied from 0 to 550 mm in 5 mm increments. A least-squares fit of the resulting data was performed to determine the coefficients $a_{n,i}$. Of note, the calibration procedure is intended to be performed without the bowtie filter, as the TIGRE toolkit removes the effects of the bowtie from projections during the log normalization step of preprocessing before the material decomposition procedure would be performed.

2.2. The Tomographic Iterative GPU-based Reconstruction Toolkit (TIGRE)

TIGRE is an open-source, Matlab-based CBCT reconstruction toolkit. It is designed to facilitate a wide variety of use cases, from algorithm development to clinical research, with the goal of connecting development work with clinical practice in an accessible way.¹⁹ TIGRE-DE extends this project by adding the ability to perform projection-space DE material decomposition. A brief schematic version of the TIGRE-DE workflow can be seen in Fig (1). The steps associated with the use of TIGRE-DE are described in the sections below.

Figure 1:

Diagram of the DE workflow as implemented in TIGRE, with preexisting functions shaded in orange and newly-developed functionality shaded in blue. The block diagram shows the general construction of the new MaterialDecomposition.m data loader function, which loads the pair of high- and low-energy datasets and outputs a single set of VM projections at the energy specified. From there, the rest of the workflow follows the reconstruction and post-processing procedures described in past works using TIGRE.^19,20 Note that the two projection sets require calling the VarianDataLoader.m function twice.

2.3. Data Acquisition

To benchmark the VM-image production procedure in TIGRE-DE, several scans were acquired of a Catphan 604 phantom (The Phantom Laboratory, Salem, NY, United States) at 80 and 140 kV. These scans were acquired sequentially using the OBI of a Varian TrueBeam linac (Varian Medical Systems, CA) in clinical treatment mode, using both full-fan and half-fan protocols. The full-fan scans were full-trajectory protocols at 11 frames per second, yielding approximately 660 projections for each energy setting while the half-fan scans were full-trajectory protocols at 15 frames per second, yielding approximately 900 projections at each energy. All scans were acquired with titanium filtration and with their respective bowtie filters in place. Full-fan scans were acquired at 80 kV (20 mA, 60 ms) and 140 kV (20 mA, 10 ms) settings. Half-fan scans were likewise acquired at 80 kV (60 mA, 25 ms) and 140 kV (75 mA, 25 ms).

2.4. Preprocessing

The raw CBCT projections from each dataset, exported in Varian’s XIM file format, were loaded into TIGRE and preprocessed using the VarianDataLoader.m module.²⁰ This module can perform standard preprocessing operations on the projection data such as scatter correction, air normalization, logarithmic normalization, beam hardening correction, and ring artifact suppression. These corrections were designed to closely replicate the procedures utilized by Varian’s proprietary iTools Reconstruction software, which has been used for similar VM-CBCT image production in previous studies.¹² Of note, due to the monoenergetic character of the VM projections and the fact that the beam hardening effect is inherently accounted for in the material decomposition procedure, a beam hardening correction is not performed for the production of VM images (Section 2.6). In practice, some residual beam hardening effects may persist through the VM image creation process, but these can be suppressed by proper selection of the VM energy.¹³

2.5. Material Decomposition and VM Projection Creation

After preprocessing, each high-energy (140 kV) projection was paired with a corresponding low-energy (80 kV) projection for material decomposition. In the present analysis, a nearest-neighbor matching scheme was employed to minimize misalignments in gantry angles between the low- and high-energy projections. Each projection pair was then decomposed, pixel-by-pixel, into equivalent thickness projections of Al and PMMA by the DeDecompose.m function using Eqs. (2) and (3). The thickness projections were then weighted by the attenuation coefficients for Al and PMMA at the desired VM energy and added to produce a single VM projection, in line with Eq. (1), with the same gantry angle as the high-energy projection.

2.6. Reconstruction and HU Mapping

The resulting set of VM projections and gantry angles can be reconstructed into a 3D volumetric image using any of the reconstruction algorithms included in the TIGRE toolkit. Currently, TIGRE includes over 20 reconstruction algorithms and variants including the classic FDK algorithm. For this work, the FDK algorithm was used to reconstruct the VM projections at the energies of 150, 100, 80, 60, 50, and 40 keV. A 3×3 median filter was used post-reconstruction to provide noise suppression.¹⁹

Post-reconstruction, HU mapping was provided using the HUMapping.m function included with the TIGRE-VarianCBCT module. This module performs a linear regression of material data with known HU values against corresponding pixel values computed in the reconstruction process, similar to the calibration procedure used clinically. The linear fit model is used to convert the image pixel values to corresponding HU values. In this case, the calibration was performed using the various material inserts of the Catphan 604 phantom.²⁰ Since the HU are energy-dependent, a different HU calibration was made for each VM energy, with the theoretical HU values for each insert and VM energy being computed from the manufacturer-reported attenuation coefficient values. Any deviations from perfect linearity between the pixel values and HU are expected to be within the 50 HU tolerance reported for the TrueBeam system.²⁵

2.7. Image Quality Evaluation

Contrast-to-noise ratios (CNRs) were computed between each material insert and the background material of the phantom via the following formula:

$$CN{R}_i=\frac{\left|H{U}_i-H{U}_{bkg}\right|}{\sqrt{\frac{1}{2}\left({\sigma }_i^2+{\sigma }_{bkg}^2\right)}}.$$ (4)

Here the subscripts $i$ and $bkg$ represent the corresponding insert and background regions-of-interest (ROIs), and $\sigma$ represents the standard deviation in the HU values within the ROIs. The images used circular ROIs with radii of approximately 8 mm centered on each material insert. The CNR values were used to assess how CNR varies with imaging energy and to compare the CNR of the VM images to the CNRs seen in CBCTs using clinical imaging protocols.

3. Results:

VM images are successfully created using the material decomposition procedure for both full-fan and half-fan CBCT scans. Reconstructed VM images of the full-fan protocol scans at different energies can be seen in Fig. (2) alongside the 80 kV and 140 kV polychromatic images and a reference 120 kV conventional CT image. The corresponding results from the half-fan reconstructions can be found in Fig. (S-1).

Figure 2:

Reconstructions of full-fan protocol images of Catphan 604 sensitometry module at 80 and 140 kV and several VM energies. A conventional CT image at 120 kV is included for reference. Beginning from the 12 o’clock position and continuing clockwise, the material inserts used are air, Teflon, Delrin at the 3 o’clock position, 20% bone, acrylic, another air insert at the 6 o’clock position, polystyrene, a background ROI at the 8 o’clock position, LDPE, 50% bone, and PMP. The apparent ring around the edge of the phantom is an artifact likely caused by an incomplete scatter correction of the bowtie filter, leading to additional estimated thickness of Al and reduced thickness of PMMA in the basis materials.^28,29 Window/Level: 2200/100

3.1. HU Consistency

For each VM image, the deviations of the measured HU values from the theoretical HU values for each insert are shown in Fig. (3) for the full-fan protocol. Full-fan HU values are overall consistent with theoretical values, with root mean squared errors (RMSE) from 9–15 HU for VM energies 50–150 keV. The 40 keV image has an RMSE of 40 HU due to large deviations from theoretical HU values in the high-density materials Teflon and 50% bone. These deviations may be attributable to high uncertainties in the object and detector scatter corrections for those inserts or due to the uncertainty in the densities and elemental compositions of the material inserts.^12,26

Figure 3:

HU consistency plot for the Catphan 604 material inserts measured with a full-fan protocol. The clinical tolerance of the TrueBeam system is ±50 HU.²⁵ Other studies that use iTools Reconstruction¹² clip HU values below −1000, which is not done here, with the result that the air HU values show residuals that may not be present in other works.

3.2. CNR

The CNR values for the various inserts are the result of competition between two main effects, contrast enhancement and noise level. For the low-Z inserts (acrylic, polystyrene, LDPE, and PMP), there is a modest contrast enhancement at energies below 100 keV compared with higher energies. In this case, the primary driver of CNR is the noise level, which reaches a minimum near 60 keV and rises sharply at lower energies, consistent with previous findings.²⁷ The high-Z inserts (Teflon, Delrin, 20%, and 50% bone) show this same effect, but also show a more significant contrast enhancement at lower energies.

CNR trends as a function of image energy for the various material inserts, as well as comparison to polychromatic kV images, for the full-fan protocol are shown in Fig. (4). The 60 keV images show substantial CNR enhancements over the constituent 80 kV and 140 kV images with average enhancements of 63% and 66%, respectively. The 60 keV half-fan images show similar improvements, as seen in Fig. (S-3).

Figure 4:

Full-fan CNR values: a) CNR of each insert as a function of VM energy, indicating that, of the energies used, 60 keV provides the highest CNR for all material inserts; b) Comparison between the CNR values for the 60 keV image and the constituent 80 kV and 140 kV images. Of note, the 60 keV image results in higher CNR values for all inserts than both polychromatic images.

4. Discussion:

The goal for this work was to implement DE-CBCT image decomposition in an accessible, open-source setting to make the development and exploration of DE tools more widely available for ongoing research and development. We validated the performance of the TIGRE-DE module by replicating the results shown by Cassetta et al.¹², showing the characteristic VM image behavior of enhanced material contrast that is consistent with other current approaches to VM-CBCT image creation.

Several works^9–13 have explored different methods for acquiring and processing DE-CBCT images. Li et al.¹³ described a procedure for optimizing the reduction of beam hardening and metal artifacts, finding that the ideal imaging energy may depend on the specific site and materials to be imaged, with metal artifacts showing optimal reduction at higher energies and non-metal beam hardening artifacts showing optimal reduction at lower energies. Others explored various ways of producing the DE scans, including multi-source scans¹³, split or alternating filters¹¹, sequential scans⁹, dual-layer detectors³⁰, and fast kV switching.¹² Of these, only Men et al. and Cassetta et al. used a commercially available linear accelerator, with the latter providing the closest match to a clinical application by including consideration of the bowtie filter. Iramina et al.¹¹ explored artifact reduction using only linear mixed images rather than VM images. Several explored the creation of VM images but used either in-house¹³ or proprietary^9,12 tools to perform their analyses.

Both this work and the work by Cassetta et al.¹² showed that VM images could provide similar contrast enhancements over polychromatic kV images, with Cassetta et al. finding average CNR enhancements of 43% and 63% over 80 kV and 140 kV images, respectively, compared with the 63% and 66% average enhancements seen here. The major innovation of this work compared to Cassetta et al. was the implementation of DE-CBCT material decomposition and VM image production in the open-source TIGRE toolkit instead of using the proprietary iTools Reconstruction package. The similar CNR enhancements between the polychromatic and VM images, taken with the same exposure settings, provides an important validation of this DE-CBCT implementation. Additionally, this work extends to consider the use of half-fan imaging protocols, which present a wider field of view than the ones that use full-fan protocols, the results of which can be seen in the supplement.

The present work has a few limitations. With respect to the TIGRE software package, the TIGRE-DE module was developed and tested using the VarianCBCT data loader, as this data loader contains preprocessing capabilities and represents the TrueBeam system that was available to the authors for data acquisition. While the TIGRE-DE functions should be acquisition-system-agnostic, some care needs to be taken when used alongside the other data loaders included in the TIGRE toolkit. In particular, the calibration procedure used to determine the $a_{n,i}$ coefficients for the material decomposition procedure includes assumptions about the behavior of the imaging system¹² that would not apply across different CBCT imaging systems from different manufacturers. End users should ensure that all steps of the DE-CBCT workflow (Fig. (1)) are well-calibrated for their imaging systems, as poor calibrations may alter the basis material thicknesses in unpredictable ways, leading to inaccurate results.

Instead of the virtual phantom used in this work, the calibration procedure can also be performed experimentally using a physical phantom consisting of sufficient combinations of Al and PMMA thicknesses. This is often performed using a step-wedge phantom.^9,13 This approach has the advantage of naturally accounting for the x-ray spectrum and the detector response that would need to be simulated for use with a virtual phantom. Care should be taken to remove as much scatter as possible from these physical calibration images, which would not be a concern with the virtual phantom.

The scatter correction implemented within the TIGRE toolkit may be insufficient to completely remove the effects of scattered radiation from the polychromatic CBCT images. The material decomposition procedure is calibrated assuming scatter-free conditions, and previous studies^28,29 have shown that the presence of unaccounted-for scatter in DE-CT can lead to systematic errors in the basis material equivalent thicknesses (Fig. 2). Typically, the thickness of the high-Z material will be overestimated, while the thickness of the low-Z material will be underestimated.²⁸ This effect would be most pronounced in the region shaded by the bowtie filter, for which there is a significant thickness of radiation-scattering material. Implementation of more robust scatter-correction methods^31,32 within TIGRE could be a valuable future addition to the toolkit.

With respect to the creation of VM images in general, this work focused mainly on presenting the new toolkit and its validation through comparison to a previous study.¹¹ No effort was made to optimize the image acquisition parameters themselves, particularly regarding the delivered imaging dose. Doses were also not matched between the polychromatic and VM images, so direct comparison between them is limited. Optimizing the VM image creation process with respect to imaging dose and mAs settings remains a significant avenue for exploration.³³

5. Conclusions:

This work introduces the TIGRE-DE toolkit, an open-source Matlab toolkit for the performance of projection-domain basis material decomposition in CBCT and the construction of VM CBCT images. A comparison to similar previous work shows the consistency of this procedure with similar implementations using proprietary software.

Supplementary Material

Fig S2

Figure S-2: HU consistency plot for the Catphan 604 material inserts measured with a half-fan protocol. The clinical tolerance for the TrueBeam system is ±50 HU.²⁵ The highest-density inserts, Teflon and 50% Bone, show significant deviations from the expected HU values at some energies, which may be attributable to uncertainties in the object and detector scatter corrections or to uncertainty in the densities and the elemental compositions of the bone inserts.^12,26

Fig S1

Figure S-1: Reconstructions of half-fan protocol Catphan 604 images at 80 and 140 kV and multiple VM energies. The analysis methodology mirrors that used for the full-fan images. Window/Level: 2200/100

Fig S3

Figure S-3: Half-fan CNR values: a) CNR as a function of VM energy, indicating that, of the energies considered, 60 keV provides the highest CNR for all material inserts; b) Comparison between the CNR values for the 60 keV image and the constituent 80 kV and 140 kV scans, showing average enhancements of 47% and 22%, respectively, for the VM image compared to the polychromatic images.